Re: Do "Normal" Taxi firms vet their drivers to this level... would think not... does anyone know?
That's is just not true, at least not in Massachusetts in the USA. First of all, the idea that Uber doesn't do a background check on drivers is false. They do and I believe that occurs throughout the US. However, Uber uses a private firm that does not have access to all records on individuals, especially those over 7 years old.
The Massachusetts legislature, in late 2016, passed a law requiring all Uber drivers pass a state-administered background check identical to those for taxi drivers. The law went into effect in January of 2017 and as a result, over 8,000 drivers (Lyft included) who failed the more intensive check were dropped.
Agreeing to a waiver allowing a background check is part of the Uber signup process, in any case. I sincerely doubt that was any different in the UK.